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Lorenz 96 Model
The Lorenz 96 model is a dynamical system formulated by Edward Lorenz in 1996. It is defined as follows. For i=1,...,N: :\frac = (x_-x_)x_ - x_i + F where it is assumed that x_=x_,x_0=x_N and x_=x_1 and N \ge 4. Here x_i is the state of the system and F is a forcing constant. F=8 is a common value known to cause chaotic behavior. It is commonly used as a model problem in data assimilation. Python simulation from mpl_toolkits.mplot3d import Axes3D from scipy.integrate import odeint import matplotlib.pyplot as plt import numpy as np # These are our constants N = 5 # Number of variables F = 8 # Forcing def L96(x, t): """Lorenz 96 model with constant forcing""" # Setting up vector d = np.zeros(N) # Loops over indices (with operations and Python underflow indexing handling edge cases) for i in range(N): d = (x i + 1) % N- x - 2 * x - 1- x + F return d x0 = F * np.ones(N) # Initial state (equilibrium) x0 += 0.01 # Add small perturbation to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Lorenz
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology. He is best known as the founder of modern chaos theory, a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. His discovery of deterministic chaos "profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton," according to the committee that awarded him the 1991 Kyoto Prize for basic sciences in the field of earth and planetary sciences. Biographical information Lorenz was born in 1917 in West Hartford, Connecticut. He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Assimilation
Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – for example, to determine the optimal state estimate of a system, to determine initial conditions for a numerical forecast model, to interpolate sparse observation data using (e.g. physical) knowledge of the system being observed, to set numerical parameters based on training a model from observed data. Depending on the goal, different solution methods may be used. Data assimilation is distinguished from other forms of machine learning, image analysis, and statistical methods in that it utilizes a dynamical model of the system being analyzed. Data assimilation initially developed in the field of numerical weather prediction. Numerical weather prediction models are equations describing the dynamical behavior of the atmosphere, typically coded into a computer program. In order to use t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorenz 96
Lorenz is an originally German name derived from the Roman surname Laurentius, which means "from Laurentum". Given name People with the given name Lorenz include: * Prince Lorenz of Belgium (born 1955), member of the Belgian royal family by his marriage with Princess Astrid of Belgium * Lorenz Böhler (1885–1973), Austrian trauma surgeon * Lorenz Hart (1895–1943), American lyricist, half of the famed Broadway songwriting team Rodgers and Hart * Lorenz Lange (1690–1752), Russian official in Siberia * Lorenz Oken (1779–1851), German naturalist * Lorenz of Werle (1338/40–1393/94), Lord of Werle-Güstrow Surname People with the name surname Lorenz include: * Adolf Lorenz (1854–1946), Austrian surgeon * Alfred Lorenz (1868–1939), Austrian-German musical analyst * Angela Lorenz (born 1965), American artist * Barbara Lorenz, make-up artist * Carl Lorenz (1913–1993), German cyclist * Christian Lorenz (born 1966), German musician * Edward Norton Lorenz (1917–2008), A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Articles With Example Python (programming Language) Code
Article often refers to: * Article (grammar), a grammatical element used to indicate definiteness or indefiniteness * Article (publishing), a piece of nonfictional prose that is an independent part of a publication Article may also refer to: Government and law * Article (European Union), articles of treaties of the European Union * Articles of association, the regulations governing a company, used in India, the UK and other countries * Articles of clerkship, the contract accepted to become an articled clerk * Articles of Confederation, the predecessor to the current United States Constitution *Article of Impeachment, a formal document and charge used for impeachment in the United States * Articles of incorporation, for corporations, U.S. equivalent of articles of association * Articles of organization, for limited liability organizations, a U.S. equivalent of articles of association Other uses * Article, an HTML element, delimited by the tags and * Article of clothing, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic Maps
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids, Cartoon Network and Disney XD. It was brought over to the United States from Denmark by Bryan C. Gannon and Chaotic USA Entertainment Group, and produced by Chaotic USA Entertainment Group, 4Kids Productions and Bardel Entertainment. The trading card game came out 6 September 2006 in the U.S. and Canada. Each card comes with a unique code which the owner can upload onto the Chaotic website. This allows the owner to trade and play online using their own card collection. The game was well known to be the only game with a TV show, an online game, and a TCG that were all integrated. However, the online game is currently closed. History Chaotic started out as a trading card game known as "Grolls and Gorks" and an idea for a cartoon series ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
